Two function algebras defining functions in NC k boolean circuits

We describe the functions computed by boolean circuits in NCk by means of func- tions algebra for k ≥ 1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic charac- terization of the complexity classes NCk for k ≥ 1 without...

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Bibliographic Details
Published in:Information and computation Vol. 248; pp. 82 - 103
Main Authors: Bonfante, Guillaume, Kahle, Reinhard, Marion, Jean-Yves, Oitavem, Isabel
Format: Journal Article
Language:English
Published: Elsevier 01.06.2016
Subjects:
Computational Complexity
Computer Science
parallel computation class
transducers
Boolean circuits
NCk
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:We describe the functions computed by boolean circuits in NCk by means of func- tions algebra for k ≥ 1 in the spirit of implicit computational complexity. The whole hierarchy defines NC. In other words, we give a recursion-theoretic charac- terization of the complexity classes NCk for k ≥ 1 without reference to a machine model, nor explicit bounds in the recursion schema. Actually, we give two equiv- alent description of the classes NCk, f ≥ 1. One is based on a tree structure a` la Leivant, the other is based on words. This latter puts into light the role of computation of pointers in circuit complexity. We show that transducers are a key concept for pointer evaluation.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2015.12.009